LMFDB - Embedded newform 845.2.e.f.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(146,845)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("845.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.146
Dual form			845.2.e.f.191.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.633975 + 1.09808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.633975 + 1.09808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-0.633975 - 1.09808i) q^{11} -0.732051 q^{12} +3.46410 q^{14} +(0.366025 + 0.633975i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-1.73205 + 3.00000i) q^{17} +4.26795 q^{18} +(2.09808 - 3.63397i) q^{19} +(-0.500000 + 0.866025i) q^{20} +1.46410 q^{21} +(1.09808 - 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(0.633975 + 1.09808i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.73205 + 8.19615i) q^{29} +(-0.633975 + 1.09808i) q^{30} +0.196152 q^{31} +(-2.59808 + 4.50000i) q^{32} +(0.464102 - 0.803848i) q^{33} -6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(1.23205 + 2.13397i) q^{36} +(-2.00000 - 3.46410i) q^{37} +7.26795 q^{38} +1.73205 q^{40} +(-1.73205 - 3.00000i) q^{41} +(1.26795 + 2.19615i) q^{42} +(-5.09808 + 8.83013i) q^{43} +1.26795 q^{44} +(1.23205 - 2.13397i) q^{45} +(4.09808 - 7.09808i) q^{46} -6.00000 q^{47} +(-1.83013 + 3.16987i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.866025 + 1.50000i) q^{50} -2.53590 q^{51} -10.3923 q^{53} +(3.46410 + 6.00000i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(1.73205 - 3.00000i) q^{56} +3.07180 q^{57} +(-8.19615 + 14.1962i) q^{58} +(-7.56218 + 13.0981i) q^{59} -0.732051 q^{60} +(-6.19615 + 10.7321i) q^{61} +(0.169873 + 0.294229i) q^{62} +(-2.46410 - 4.26795i) q^{63} +1.00000 q^{64} +1.60770 q^{66} +(-7.19615 - 12.4641i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(1.73205 - 3.00000i) q^{69} +3.46410 q^{70} +(0.633975 - 1.09808i) q^{71} +(2.13397 - 3.69615i) q^{72} +4.00000 q^{73} +(3.46410 - 6.00000i) q^{74} +(0.366025 + 0.633975i) q^{75} +(2.09808 + 3.63397i) q^{76} -2.53590 q^{77} +12.3923 q^{79} +(2.50000 + 4.33013i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-0.732051 + 1.26795i) q^{84} +(-1.73205 + 3.00000i) q^{85} -17.6603 q^{86} +(-3.46410 + 6.00000i) q^{87} +(-1.09808 - 1.90192i) q^{88} +(0.464102 + 0.803848i) q^{89} +4.26795 q^{90} +4.73205 q^{92} +(0.0717968 + 0.124356i) q^{93} +(-5.19615 - 9.00000i) q^{94} +(2.09808 - 3.63397i) q^{95} -3.80385 q^{96} +(1.00000 - 1.73205i) q^{97} +(-2.59808 + 4.50000i) q^{98} -3.12436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 2 q^{15} + 10 q^{16} + 24 q^{18} - 2 q^{19} - 2 q^{20} - 8 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} + 4 q^{25} + 16 q^{27} + 4 q^{28} + 12 q^{29} - 6 q^{30} - 20 q^{31} - 12 q^{33} - 24 q^{34} + 4 q^{35} - 2 q^{36} - 8 q^{37} + 36 q^{38} + 12 q^{42} - 10 q^{43} + 12 q^{44} - 2 q^{45} + 6 q^{46} - 24 q^{47} + 10 q^{48} + 6 q^{49} - 24 q^{51} - 6 q^{55} + 40 q^{57} - 12 q^{58} - 6 q^{59} + 4 q^{60} - 4 q^{61} + 18 q^{62} + 4 q^{63} + 4 q^{64} + 48 q^{66} - 8 q^{67} + 6 q^{71} + 12 q^{72} + 16 q^{73} - 2 q^{75} - 2 q^{76} - 24 q^{77} + 8 q^{79} + 10 q^{80} - 2 q^{81} + 12 q^{82} + 24 q^{83} + 4 q^{84} - 36 q^{86} + 6 q^{88} - 12 q^{89} + 24 q^{90} + 12 q^{92} + 28 q^{93} - 2 q^{95} - 36 q^{96} + 4 q^{97} + 36 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 2 * q^15 + 10 * q^16 + 24 * q^18 - 2 * q^19 - 2 * q^20 - 8 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 + 4 * q^25 + 16 * q^27 + 4 * q^28 + 12 * q^29 - 6 * q^30 - 20 * q^31 - 12 * q^33 - 24 * q^34 + 4 * q^35 - 2 * q^36 - 8 * q^37 + 36 * q^38 + 12 * q^42 - 10 * q^43 + 12 * q^44 - 2 * q^45 + 6 * q^46 - 24 * q^47 + 10 * q^48 + 6 * q^49 - 24 * q^51 - 6 * q^55 + 40 * q^57 - 12 * q^58 - 6 * q^59 + 4 * q^60 - 4 * q^61 + 18 * q^62 + 4 * q^63 + 4 * q^64 + 48 * q^66 - 8 * q^67 + 6 * q^71 + 12 * q^72 + 16 * q^73 - 2 * q^75 - 2 * q^76 - 24 * q^77 + 8 * q^79 + 10 * q^80 - 2 * q^81 + 12 * q^82 + 24 * q^83 + 4 * q^84 - 36 * q^86 + 6 * q^88 - 12 * q^89 + 24 * q^90 + 12 * q^92 + 28 * q^93 - 2 * q^95 - 36 * q^96 + 4 * q^97 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.633975	+	1.09808i	−0.258819	+	0.448288i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	1.73205			0.612372
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	0.866025	+	1.50000i	0.273861	+	0.474342i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	−0.732051			−0.211325
$13$		0			0
$13$		0			0
$14$	3.46410			0.925820
$15$	0.366025	+	0.633975i	0.0945074	+	0.163692i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	−0.995947	−	0.0899392i	$-0.971333\pi$
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	0.575863	+	0.817546i	$0.304666\pi$
$18$	4.26795			1.00597
$19$	2.09808	−	3.63397i	0.481332	−	0.833691i	−0.518439	−	0.855115i	$-0.673487\pi$
$19$	2.09808	−	3.63397i	0.481332	−	0.833691i	0.999770	+	0.0214238i	$0.00681993\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	1.46410			0.319493
$22$	1.09808	−	1.90192i	0.234111	−	0.405492i
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	0.506620	−	0.862169i	$-0.330895\pi$
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	−0.999971	+	0.00766135i	$0.997561\pi$
$24$	0.633975	+	1.09808i	0.129410	+	0.224144i
$25$	1.00000			0.200000
$26$		0			0
$27$	4.00000			0.769800
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	4.73205	+	8.19615i	0.878720	+	1.52199i	0.852747	+	0.522325i	$0.174935\pi$
$29$	4.73205	+	8.19615i	0.878720	+	1.52199i	0.0259731	+	0.999663i	$0.491732\pi$
$30$	−0.633975	+	1.09808i	−0.115747	+	0.200480i
$31$	0.196152			0.0352300			0.0176150	−	0.999845i	$-0.494393\pi$
$31$	0.196152			0.0352300			0.0176150	+	0.999845i	$0.494393\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	0.464102	−	0.803848i	0.0807897	−	0.139932i
$34$	−6.00000			−1.02899
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	1.23205	+	2.13397i	0.205342	+	0.355662i
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	7.26795			1.17902
$39$		0			0
$40$	1.73205			0.273861
$41$	−1.73205	−	3.00000i	−0.270501	−	0.468521i	0.698489	−	0.715621i	$-0.253856\pi$
$41$	−1.73205	−	3.00000i	−0.270501	−	0.468521i	−0.968990	+	0.247099i	$0.920523\pi$
$42$	1.26795	+	2.19615i	0.195649	+	0.338874i
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	0.155958	+	0.987764i	$0.450153\pi$
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	−0.933408	+	0.358818i	$0.883180\pi$
$44$	1.26795			0.191151
$45$	1.23205	−	2.13397i	0.183663	−	0.318114i
$46$	4.09808	−	7.09808i	0.604228	−	1.04655i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−1.83013	+	3.16987i	−0.264156	+	0.457532i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.866025	+	1.50000i	0.122474	+	0.212132i
$51$	−2.53590			−0.355097
$52$		0			0
$53$	−10.3923			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$53$	−10.3923			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$54$	3.46410	+	6.00000i	0.471405	+	0.816497i
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	1.73205	−	3.00000i	0.231455	−	0.400892i
$57$	3.07180			0.406869
$58$	−8.19615	+	14.1962i	−1.07621	+	1.86405i
$59$	−7.56218	+	13.0981i	−0.984512	+	1.70522i	−0.340425	+	0.940272i	$0.610571\pi$
$59$	−7.56218	+	13.0981i	−0.984512	+	1.70522i	−0.644086	+	0.764953i	$0.722762\pi$
$60$	−0.732051			−0.0945074
$61$	−6.19615	+	10.7321i	−0.793336	+	1.37410i	0.130554	+	0.991441i	$0.458324\pi$
$61$	−6.19615	+	10.7321i	−0.793336	+	1.37410i	−0.923890	+	0.382657i	$0.875009\pi$
$62$	0.169873	+	0.294229i	0.0215739	+	0.0373671i
$63$	−2.46410	−	4.26795i	−0.310448	−	0.537711i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.60770			0.197894
$67$	−7.19615	−	12.4641i	−0.879150	−	1.52273i	−0.852275	−	0.523094i	$-0.824778\pi$
$67$	−7.19615	−	12.4641i	−0.879150	−	1.52273i	−0.0268747	−	0.999639i	$-0.508556\pi$
$68$	−1.73205	−	3.00000i	−0.210042	−	0.363803i
$69$	1.73205	−	3.00000i	0.208514	−	0.361158i
$70$	3.46410			0.414039
$71$	0.633975	−	1.09808i	0.0752389	−	0.130318i	−0.825951	−	0.563742i	$-0.809361\pi$
$71$	0.633975	−	1.09808i	0.0752389	−	0.130318i	0.901190	+	0.433424i	$0.142695\pi$
$72$	2.13397	−	3.69615i	0.251491	−	0.435596i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	3.46410	−	6.00000i	0.402694	−	0.697486i
$75$	0.366025	+	0.633975i	0.0422650	+	0.0732051i
$76$	2.09808	+	3.63397i	0.240666	+	0.416845i
$77$	−2.53590			−0.288992
$78$		0			0
$79$	12.3923			1.39424			0.697122	−	0.716953i	$-0.254464\pi$
$79$	12.3923			1.39424			0.697122	+	0.716953i	$0.254464\pi$
$80$	2.50000	+	4.33013i	0.279508	+	0.484123i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−0.732051	+	1.26795i	−0.0798733	+	0.138345i
$85$	−1.73205	+	3.00000i	−0.187867	+	0.325396i
$86$	−17.6603			−1.90435
$87$	−3.46410	+	6.00000i	−0.371391	+	0.643268i
$88$	−1.09808	−	1.90192i	−0.117055	−	0.202746i
$89$	0.464102	+	0.803848i	0.0491947	+	0.0852077i	0.889574	−	0.456791i	$-0.151001\pi$
$89$	0.464102	+	0.803848i	0.0491947	+	0.0852077i	−0.840379	+	0.541998i	$0.817668\pi$
$90$	4.26795			0.449881
$91$		0			0
$92$	4.73205			0.493350
$93$	0.0717968	+	0.124356i	0.00744498	+	0.0128951i
$94$	−5.19615	−	9.00000i	−0.535942	−	0.928279i
$95$	2.09808	−	3.63397i	0.215258	−	0.372838i
$96$	−3.80385			−0.388229
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−2.59808	+	4.50000i	−0.262445	+	0.454569i
$99$	−3.12436			−0.314010
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.46410	−	11.1962i	−0.643202	−	1.11406i	−0.984714	−	0.174181i	$-0.944272\pi$
$101$	−6.46410	−	11.1962i	−0.643202	−	1.11406i	0.341511	−	0.939878i	$-0.389061\pi$
$102$	−2.19615	−	3.80385i	−0.217451	−	0.376637i
$103$	10.1962			1.00466			0.502328	−	0.864677i	$-0.332477\pi$
$103$	10.1962			1.00466			0.502328	+	0.864677i	$0.332477\pi$
$104$		0			0
$105$	1.46410			0.142882
$106$	−9.00000	−	15.5885i	−0.874157	−	1.51408i
$107$	−0.169873	−	0.294229i	−0.0164222	−	0.0284442i	0.857697	−	0.514155i	$-0.171894\pi$
$107$	−0.169873	−	0.294229i	−0.0164222	−	0.0284442i	−0.874120	+	0.485710i	$0.838561\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.09808	−	1.90192i	0.104697	−	0.181341i
$111$	1.46410	−	2.53590i	0.138966	−	0.240697i
$112$	10.0000			0.944911
$113$	−7.73205	+	13.3923i	−0.727370	+	1.25984i	0.230621	+	0.973044i	$0.425924\pi$
$113$	−7.73205	+	13.3923i	−0.727370	+	1.25984i	−0.957991	+	0.286798i	$0.907409\pi$
$114$	2.66025	+	4.60770i	0.249156	+	0.431550i
$115$	−2.36603	−	4.09808i	−0.220633	−	0.382148i
$116$	−9.46410			−0.878720
$117$		0			0
$118$	−26.1962			−2.41155
$119$	3.46410	+	6.00000i	0.317554	+	0.550019i
$120$	0.633975	+	1.09808i	0.0578737	+	0.100240i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	−21.4641			−1.94327
$123$	1.26795	−	2.19615i	0.114327	−	0.198020i
$124$	−0.0980762	+	0.169873i	−0.00880750	+	0.0152550i
$125$	1.00000			0.0894427
$126$	4.26795	−	7.39230i	0.380219	−	0.658559i
$127$	−2.90192	−	5.02628i	−0.257504	−	0.446010i	0.708069	−	0.706144i	$-0.249567\pi$
$127$	−2.90192	−	5.02628i	−0.257504	−	0.446010i	−0.965573	+	0.260134i	$0.916233\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	−7.46410			−0.657178
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	0.464102	+	0.803848i	0.0403949	+	0.0699660i
$133$	−4.19615	−	7.26795i	−0.363853	−	0.630211i
$134$	12.4641	−	21.5885i	1.07673	−	1.86496i
$135$	4.00000			0.344265
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−6.46410	+	11.1962i	−0.552265	+	0.956552i	0.445845	+	0.895110i	$0.352903\pi$
$137$	−6.46410	+	11.1962i	−0.552265	+	0.956552i	−0.998111	+	0.0614418i	$0.980430\pi$
$138$	6.00000			0.510754
$139$	4.19615	−	7.26795i	0.355913	−	0.616459i	−0.631361	−	0.775489i	$-0.717503\pi$
$139$	4.19615	−	7.26795i	0.355913	−	0.616459i	0.987274	+	0.159030i	$0.0508366\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	−2.19615	−	3.80385i	−0.184949	−	0.320342i
$142$	2.19615			0.184297
$143$		0			0
$144$	12.3205			1.02671
$145$	4.73205	+	8.19615i	0.392975	+	0.680653i
$146$	3.46410	+	6.00000i	0.286691	+	0.496564i
$147$	−1.09808	+	1.90192i	−0.0905678	+	0.156868i
$148$	4.00000			0.328798
$149$	9.92820	−	17.1962i	0.813350	−	1.40876i	−0.0971565	−	0.995269i	$-0.530975\pi$
$149$	9.92820	−	17.1962i	0.813350	−	1.40876i	0.910507	−	0.413495i	$-0.135692\pi$
$150$	−0.633975	+	1.09808i	−0.0517638	+	0.0896575i
$151$	12.1962			0.992509			0.496254	−	0.868177i	$-0.334708\pi$
$151$	12.1962			0.992509			0.496254	+	0.868177i	$0.334708\pi$
$152$	3.63397	−	6.29423i	0.294754	−	0.510529i
$153$	4.26795	+	7.39230i	0.345043	+	0.597632i
$154$	−2.19615	−	3.80385i	−0.176971	−	0.306523i
$155$	0.196152			0.0157553
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	10.7321	+	18.5885i	0.853796	+	1.47882i
$159$	−3.80385	−	6.58846i	−0.301665	−	0.522499i
$160$	−2.59808	+	4.50000i	−0.205396	+	0.355756i
$161$	−9.46410			−0.745876
$162$	3.86603	−	6.69615i	0.303744	−	0.526099i
$163$	3.19615	−	5.53590i	0.250342	−	0.433605i	−0.713278	−	0.700881i	$-0.752790\pi$
$163$	3.19615	−	5.53590i	0.250342	−	0.433605i	0.963620	+	0.267276i	$0.0861236\pi$
$164$	3.46410			0.270501
$165$	0.464102	−	0.803848i	0.0361303	−	0.0625794i
$166$	5.19615	+	9.00000i	0.403300	+	0.698535i
$167$	6.46410	+	11.1962i	0.500207	+	0.866384i	1.00000		0.000239271i	$7.61624e-5\pi$
$167$	6.46410	+	11.1962i	0.500207	+	0.866384i	−0.499793	+	0.866145i	$0.666591\pi$
$168$	2.53590			0.195649
$169$		0			0
$170$	−6.00000			−0.460179
$171$	−5.16987	−	8.95448i	−0.395350	−	0.684766i
$172$	−5.09808	−	8.83013i	−0.388725	−	0.673291i
$173$	−7.73205	+	13.3923i	−0.587857	+	1.01820i	0.406656	+	0.913581i	$0.366695\pi$
$173$	−7.73205	+	13.3923i	−0.587857	+	1.01820i	−0.994513	+	0.104617i	$0.966638\pi$
$174$	−12.0000			−0.909718
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	3.16987	−	5.49038i	0.238938	−	0.413853i
$177$	−11.0718			−0.832207
$178$	−0.803848	+	1.39230i	−0.0602509	+	0.104358i
$179$	2.53590	+	4.39230i	0.189542	+	0.328296i	0.945098	−	0.326788i	$-0.105966\pi$
$179$	2.53590	+	4.39230i	0.189542	+	0.328296i	−0.755556	+	0.655084i	$0.772633\pi$
$180$	1.23205	+	2.13397i	0.0918316	+	0.159057i
$181$	−20.3923			−1.51575			−0.757874	−	0.652401i	$-0.773762\pi$
$181$	−20.3923			−1.51575			−0.757874	+	0.652401i	$0.773762\pi$
$182$		0			0
$183$	−9.07180			−0.670607
$184$	−4.09808	−	7.09808i	−0.302114	−	0.523277i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	−0.124356	+	0.215390i	−0.00911820	+	0.0157932i
$187$	4.39230			0.321197
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	4.00000	−	6.92820i	0.290957	−	0.503953i
$190$	7.26795			0.527272
$191$	9.46410	−	16.3923i	0.684798	−	1.18611i	−0.288702	−	0.957419i	$-0.593224\pi$
$191$	9.46410	−	16.3923i	0.684798	−	1.18611i	0.973500	−	0.228686i	$-0.0734431\pi$
$192$	0.366025	+	0.633975i	0.0264156	+	0.0457532i
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$	3.46410			0.248708
$195$		0			0
$196$	−3.00000			−0.214286
$197$	0.464102	+	0.803848i	0.0330659	+	0.0572718i	0.882085	−	0.471091i	$-0.156140\pi$
$197$	0.464102	+	0.803848i	0.0330659	+	0.0572718i	−0.849019	+	0.528362i	$0.822806\pi$
$198$	−2.70577	−	4.68653i	−0.192291	−	0.333057i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	1.73205			0.122474
$201$	5.26795	−	9.12436i	0.371572	−	0.643582i
$202$	11.1962	−	19.3923i	0.787759	−	1.36444i
$203$	18.9282			1.32850
$204$	1.26795	−	2.19615i	0.0887742	−	0.153761i
$205$	−1.73205	−	3.00000i	−0.120972	−	0.209529i
$206$	8.83013	+	15.2942i	0.615224	+	1.06560i
$207$	−11.6603			−0.810444
$208$		0			0
$209$	−5.32051			−0.368027
$210$	1.26795	+	2.19615i	0.0874968	+	0.151549i
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	5.19615	−	9.00000i	0.356873	−	0.618123i
$213$	0.928203			0.0635994
$214$	0.294229	−	0.509619i	0.0201131	−	0.0348368i
$215$	−5.09808	+	8.83013i	−0.347686	+	0.602210i
$216$	6.92820			0.471405
$217$	0.196152	−	0.339746i	0.0133157	−	0.0230635i
$218$	−1.73205	−	3.00000i	−0.117309	−	0.203186i
$219$	1.46410	+	2.53590i	0.0989348	+	0.171360i
$220$	1.26795			0.0854851
$221$		0			0
$222$	5.07180			0.340397
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	5.19615	+	9.00000i	0.347183	+	0.601338i
$225$	1.23205	−	2.13397i	0.0821367	−	0.142265i
$226$	−26.7846			−1.78169
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	−0.802804	−	0.596244i	$-0.796659\pi$
$227$	1.73205	−	3.00000i	0.114960	−	0.199117i	0.917764	+	0.397127i	$0.129993\pi$
$228$	−1.53590	+	2.66025i	−0.101717	+	0.176180i
$229$	14.3923			0.951070			0.475535	−	0.879697i	$-0.342254\pi$
$229$	14.3923			0.951070			0.475535	+	0.879697i	$0.342254\pi$
$230$	4.09808	−	7.09808i	0.270219	−	0.468033i
$231$	−0.928203	−	1.60770i	−0.0610713	−	0.105779i
$232$	8.19615	+	14.1962i	0.538104	+	0.932023i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	−7.56218	−	13.0981i	−0.492256	−	0.852612i
$237$	4.53590	+	7.85641i	0.294638	+	0.510328i
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	3.80385			0.246050			0.123025	−	0.992404i	$-0.460740\pi$
$239$	3.80385			0.246050			0.123025	+	0.992404i	$0.460740\pi$
$240$	−1.83013	+	3.16987i	−0.118134	+	0.204614i
$241$	9.19615	−	15.9282i	0.592376	−	1.02603i	−0.401535	−	0.915844i	$-0.631523\pi$
$241$	9.19615	−	15.9282i	0.592376	−	1.02603i	0.993911	−	0.110182i	$-0.0351434\pi$
$242$	16.2679			1.04574
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$	−6.19615	−	10.7321i	−0.396668	−	0.687049i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$	4.39230			0.280043
$247$		0			0
$248$	0.339746			0.0215739
$249$	2.19615	+	3.80385i	0.139176	+	0.241059i
$250$	0.866025	+	1.50000i	0.0547723	+	0.0948683i
$251$	7.26795	−	12.5885i	0.458749	−	0.794576i	−0.540146	−	0.841571i	$-0.681631\pi$
$251$	7.26795	−	12.5885i	0.458749	−	0.794576i	0.998895	+	0.0469948i	$0.0149644\pi$
$252$	4.92820			0.310448
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	5.02628	−	8.70577i	0.315377	−	0.546249i
$255$	−2.53590			−0.158804
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.92820	+	6.80385i	0.245035	+	0.424412i	0.962141	−	0.272551i	$-0.0878673\pi$
$257$	3.92820	+	6.80385i	0.245035	+	0.424412i	−0.717107	+	0.696963i	$0.754534\pi$
$258$	−6.46410	−	11.1962i	−0.402437	−	0.697042i
$259$	−8.00000			−0.497096
$260$		0			0
$261$	23.3205			1.44350
$262$		0			0
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	0.783811	−	0.620999i	$-0.213273\pi$
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	−0.929707	+	0.368301i	$0.879940\pi$
$264$	0.803848	−	1.39230i	0.0494734	−	0.0856904i
$265$	−10.3923			−0.638394
$266$	7.26795	−	12.5885i	0.445627	−	0.771848i
$267$	−0.339746	+	0.588457i	−0.0207921	+	0.0360130i
$268$	14.3923			0.879150
$269$	−3.92820	+	6.80385i	−0.239507	+	0.414838i	−0.960573	−	0.278028i	$-0.910319\pi$
$269$	−3.92820	+	6.80385i	−0.239507	+	0.414838i	0.721066	+	0.692866i	$0.243652\pi$
$270$	3.46410	+	6.00000i	0.210819	+	0.365148i
$271$	−10.4904	−	18.1699i	−0.637245	−	1.10374i	−0.986035	−	0.166540i	$-0.946740\pi$
$271$	−10.4904	−	18.1699i	−0.637245	−	1.10374i	0.348789	−	0.937201i	$-0.386593\pi$
$272$	−17.3205			−1.05021
$273$		0			0
$274$	−22.3923			−1.35277
$275$	−0.633975	−	1.09808i	−0.0382301	−	0.0662165i
$276$	1.73205	+	3.00000i	0.104257	+	0.180579i
$277$	2.80385	−	4.85641i	0.168467	−	0.291793i	−0.769414	−	0.638750i	$-0.779452\pi$
$277$	2.80385	−	4.85641i	0.168467	−	0.291793i	0.937881	+	0.346957i	$0.112785\pi$
$278$	14.5359			0.871805
$279$	0.241670	−	0.418584i	0.0144684	−	0.0250600i
$280$	1.73205	−	3.00000i	0.103510	−	0.179284i
$281$	−1.60770			−0.0959071			−0.0479535	−	0.998850i	$-0.515270\pi$
$281$	−1.60770			−0.0959071			−0.0479535	+	0.998850i	$0.515270\pi$
$282$	3.80385	−	6.58846i	0.226516	−	0.392337i
$283$	−0.705771	−	1.22243i	−0.0419538	−	0.0726660i	0.844286	−	0.535893i	$-0.180025\pi$
$283$	−0.705771	−	1.22243i	−0.0419538	−	0.0726660i	−0.886240	+	0.463227i	$0.846692\pi$
$284$	0.633975	+	1.09808i	0.0376195	+	0.0651588i
$285$	3.07180			0.181958
$286$		0			0
$287$	−6.92820			−0.408959
$288$	6.40192	+	11.0885i	0.377237	+	0.653394i
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$	−8.19615	+	14.1962i	−0.481295	+	0.833627i
$291$	1.46410			0.0858272
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−9.46410	+	16.3923i	−0.552899	+	0.957649i	0.445165	+	0.895449i	$0.353145\pi$
$293$	−9.46410	+	16.3923i	−0.552899	+	0.957649i	−0.998064	+	0.0622001i	$0.980188\pi$
$294$	−3.80385			−0.221845
$295$	−7.56218	+	13.0981i	−0.440287	+	0.762599i
$296$	−3.46410	−	6.00000i	−0.201347	−	0.348743i
$297$	−2.53590	−	4.39230i	−0.147148	−	0.254867i
$298$	34.3923			1.99229
$299$		0			0
$300$	−0.732051			−0.0422650
$301$	10.1962	+	17.6603i	0.587696	+	1.01792i
$302$	10.5622	+	18.2942i	0.607785	+	1.05271i
$303$	4.73205	−	8.19615i	0.271849	−	0.470857i
$304$	20.9808			1.20333
$305$	−6.19615	+	10.7321i	−0.354791	+	0.614515i
$306$	−7.39230	+	12.8038i	−0.422590	+	0.731947i
$307$	−22.7846			−1.30039			−0.650193	−	0.759769i	$-0.725312\pi$
$307$	−22.7846			−1.30039			−0.650193	+	0.759769i	$0.725312\pi$
$308$	1.26795	−	2.19615i	0.0722481	−	0.125137i
$309$	3.73205	+	6.46410i	0.212309	+	0.367730i
$310$	0.169873	+	0.294229i	0.00964814	+	0.0167111i
$311$	4.39230			0.249065			0.124532	−	0.992216i	$-0.460257\pi$
$311$	4.39230			0.249065			0.124532	+	0.992216i	$0.460257\pi$
$312$		0			0
$313$	6.39230			0.361314			0.180657	−	0.983546i	$-0.442178\pi$
$313$	6.39230			0.361314			0.180657	+	0.983546i	$0.442178\pi$
$314$	−8.66025	−	15.0000i	−0.488726	−	0.846499i
$315$	−2.46410	−	4.26795i	−0.138836	−	0.240472i
$316$	−6.19615	+	10.7321i	−0.348561	+	0.603725i
$317$	−24.0000			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$318$	6.58846	−	11.4115i	0.369462	−	0.639928i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$	1.00000			0.0559017
$321$	0.124356	−	0.215390i	0.00694086	−	0.0120219i
$322$	−8.19615	−	14.1962i	−0.456754	−	0.791121i
$323$	7.26795	+	12.5885i	0.404400	+	0.700440i
$324$	4.46410			0.248006
$325$		0			0
$326$	11.0718			0.613210
$327$	−0.732051	−	1.26795i	−0.0404825	−	0.0701178i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	1.60770			0.0885007
$331$	−14.2942	+	24.7583i	−0.785682	+	1.36084i	0.142909	+	0.989736i	$0.454354\pi$
$331$	−14.2942	+	24.7583i	−0.785682	+	1.36084i	−0.928591	+	0.371105i	$0.878979\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$	−9.85641			−0.540128
$334$	−11.1962	+	19.3923i	−0.612626	+	1.06110i
$335$	−7.19615	−	12.4641i	−0.393168	−	0.680987i
$336$	3.66025	+	6.33975i	0.199683	+	0.345861i
$337$	−5.60770			−0.305471			−0.152735	−	0.988267i	$-0.548808\pi$
$337$	−5.60770			−0.305471			−0.152735	+	0.988267i	$0.548808\pi$
$338$		0			0
$339$	−11.3205			−0.614846
$340$	−1.73205	−	3.00000i	−0.0939336	−	0.162698i
$341$	−0.124356	−	0.215390i	−0.00673424	−	0.0116640i
$342$	8.95448	−	15.5096i	0.484203	−	0.838664i
$343$	20.0000			1.07990
$344$	−8.83013	+	15.2942i	−0.476089	+	0.824610i
$345$	1.73205	−	3.00000i	0.0932505	−	0.161515i
$346$	−26.7846			−1.43995
$347$	−5.83013	+	10.0981i	−0.312978	+	0.542093i	−0.979006	−	0.203834i	$-0.934660\pi$
$347$	−5.83013	+	10.0981i	−0.312978	+	0.542093i	0.666028	+	0.745927i	$0.267993\pi$
$348$	−3.46410	−	6.00000i	−0.185695	−	0.321634i
$349$	3.19615	+	5.53590i	0.171086	+	0.296330i	0.938800	−	0.344463i	$-0.111939\pi$
$349$	3.19615	+	5.53590i	0.171086	+	0.296330i	−0.767714	+	0.640793i	$0.778606\pi$
$350$	3.46410			0.185164
$351$		0			0
$352$	6.58846			0.351166
$353$	13.8564	+	24.0000i	0.737502	+	1.27739i	0.953617	+	0.301023i	$0.0973281\pi$
$353$	13.8564	+	24.0000i	0.737502	+	1.27739i	−0.216115	+	0.976368i	$0.569339\pi$
$354$	−9.58846	−	16.6077i	−0.509621	−	0.882689i
$355$	0.633975	−	1.09808i	0.0336479	−	0.0582798i
$356$	−0.928203			−0.0491947
$357$	−2.53590	+	4.39230i	−0.134214	+	0.232465i
$358$	−4.39230	+	7.60770i	−0.232141	+	0.402079i
$359$	−8.19615			−0.432576			−0.216288	−	0.976330i	$-0.569395\pi$
$359$	−8.19615			−0.432576			−0.216288	+	0.976330i	$0.569395\pi$
$360$	2.13397	−	3.69615i	0.112470	−	0.194804i
$361$	0.696152	+	1.20577i	0.0366396	+	0.0634617i
$362$	−17.6603	−	30.5885i	−0.928202	−	1.60769i
$363$	6.87564			0.360878
$364$		0			0
$365$	4.00000			0.209370
$366$	−7.85641	−	13.6077i	−0.410661	−	0.711286i
$367$	−11.0981	−	19.2224i	−0.579315	−	1.00340i	−0.995558	−	0.0941495i	$-0.969987\pi$
$367$	−11.0981	−	19.2224i	−0.579315	−	1.00340i	0.416243	−	0.909253i	$-0.363346\pi$
$368$	11.8301	−	20.4904i	0.616688	−	1.06813i
$369$	−8.53590			−0.444361
$370$	3.46410	−	6.00000i	0.180090	−	0.311925i
$371$	−10.3923	+	18.0000i	−0.539542	+	0.934513i
$372$	−0.143594			−0.00744498
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	3.80385	+	6.58846i	0.196692	+	0.340681i
$375$	0.366025	+	0.633975i	0.0189015	+	0.0327383i
$376$	−10.3923			−0.535942
$377$		0			0
$378$	13.8564			0.712697
$379$	−16.4904	−	28.5622i	−0.847054	−	1.46714i	−0.883825	−	0.467817i	$-0.845041\pi$
$379$	−16.4904	−	28.5622i	−0.847054	−	1.46714i	0.0367715	−	0.999324i	$-0.488293\pi$
$380$	2.09808	+	3.63397i	0.107629	+	0.186419i
$381$	2.12436	−	3.67949i	0.108834	−	0.188506i
$382$	32.7846			1.67741
$383$	−0.464102	+	0.803848i	−0.0237145	+	0.0410747i	−0.877639	−	0.479322i	$-0.840883\pi$
$383$	−0.464102	+	0.803848i	−0.0237145	+	0.0410747i	0.853925	+	0.520397i	$0.174216\pi$
$384$	−4.43782	+	7.68653i	−0.226467	+	0.392252i
$385$	−2.53590			−0.129241
$386$	8.66025	−	15.0000i	0.440795	−	0.763480i
$387$	12.5622	+	21.7583i	0.638571	+	1.10604i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	16.3923			0.828994
$392$	2.59808	+	4.50000i	0.131223	+	0.227284i
$393$		0			0
$394$	−0.803848	+	1.39230i	−0.0404973	+	0.0701433i
$395$	12.3923			0.623525
$396$	1.56218	−	2.70577i	0.0785024	−	0.135970i
$397$	−6.39230	+	11.0718i	−0.320821	+	0.555678i	−0.980658	−	0.195731i	$-0.937292\pi$
$397$	−6.39230	+	11.0718i	−0.320821	+	0.555678i	0.659837	+	0.751409i	$0.270625\pi$
$398$	−34.6410			−1.73640
$399$	3.07180	−	5.32051i	0.153782	−	0.266359i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−11.5359	−	19.9808i	−0.576075	−	0.997792i	−0.995924	−	0.0901975i	$-0.971250\pi$
$401$	−11.5359	−	19.9808i	−0.576075	−	0.997792i	0.419849	−	0.907594i	$-0.362083\pi$
$402$	18.2487			0.910163
$403$		0			0
$404$	12.9282			0.643202
$405$	−2.23205	−	3.86603i	−0.110911	−	0.192104i
$406$	16.3923	+	28.3923i	0.813536	+	1.40909i
$407$	−2.53590	+	4.39230i	−0.125700	+	0.217718i
$408$	−4.39230			−0.217451
$409$	−19.1962	+	33.2487i	−0.949189	+	1.64404i	−0.202049	+	0.979375i	$0.564760\pi$
$409$	−19.1962	+	33.2487i	−0.949189	+	1.64404i	−0.747139	+	0.664668i	$0.768573\pi$
$410$	3.00000	−	5.19615i	0.148159	−	0.256620i
$411$	−9.46410			−0.466830
$412$	−5.09808	+	8.83013i	−0.251164	+	0.435029i
$413$	15.1244	+	26.1962i	0.744221	+	1.28903i
$414$	−10.0981	−	17.4904i	−0.496293	−	0.859605i
$415$	6.00000			0.294528
$416$		0			0
$417$	6.14359			0.300853
$418$	−4.60770	−	7.98076i	−0.225370	−	0.390352i
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	0.958154	−	0.286252i	$-0.0924094\pi$
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	−0.726979	+	0.686660i	$0.759076\pi$
$420$	−0.732051	+	1.26795i	−0.0357204	+	0.0618696i
$421$	−10.7846			−0.525610			−0.262805	−	0.964849i	$-0.584648\pi$
$421$	−10.7846			−0.525610			−0.262805	+	0.964849i	$0.584648\pi$
$422$	6.92820	−	12.0000i	0.337260	−	0.584151i
$423$	−7.39230	+	12.8038i	−0.359426	+	0.622544i
$424$	−18.0000			−0.874157
$425$	−1.73205	+	3.00000i	−0.0840168	+	0.145521i
$426$	0.803848	+	1.39230i	0.0389465	+	0.0674574i
$427$	12.3923	+	21.4641i	0.599706	+	1.03872i
$428$	0.339746			0.0164222
$429$		0			0
$430$	−17.6603			−0.851653
$431$	9.75833	+	16.9019i	0.470042	+	0.814137i	0.999413	−	0.0342535i	$-0.0109053\pi$
$431$	9.75833	+	16.9019i	0.470042	+	0.814137i	−0.529371	+	0.848390i	$0.677572\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	3.39230	−	5.87564i	0.163024	−	0.282365i	−0.772928	−	0.634494i	$-0.781209\pi$
$433$	3.39230	−	5.87564i	0.163024	−	0.282365i	0.935952	+	0.352128i	$0.114542\pi$
$434$	0.679492			0.0326167
$435$	−3.46410	+	6.00000i	−0.166091	+	0.287678i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−19.8564			−0.949861
$438$	−2.53590	+	4.39230i	−0.121170	+	0.209872i
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	−0.940963	−	0.338508i	$-0.890078\pi$
$439$	−16.0000	−	27.7128i	−0.763638	−	1.32266i	0.177325	−	0.984152i	$-0.443256\pi$
$440$	−1.09808	−	1.90192i	−0.0523487	−	0.0906707i
$441$	7.39230			0.352015
$442$		0			0
$443$	34.9808			1.66199			0.830993	−	0.556283i	$-0.187773\pi$
$443$	34.9808			1.66199			0.830993	+	0.556283i	$0.187773\pi$
$444$	1.46410	+	2.53590i	0.0694832	+	0.120348i
$445$	0.464102	+	0.803848i	0.0220005	+	0.0381060i
$446$	−1.73205	+	3.00000i	−0.0820150	+	0.142054i
$447$	14.5359			0.687524
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	13.7321	−	23.7846i	0.648056	−	1.12247i	−0.335531	−	0.942029i	$-0.608916\pi$
$449$	13.7321	−	23.7846i	0.648056	−	1.12247i	0.983587	−	0.180436i	$-0.0577509\pi$
$450$	4.26795			0.201193
$451$	−2.19615	+	3.80385i	−0.103413	+	0.179116i
$452$	−7.73205	−	13.3923i	−0.363685	−	0.629921i
$453$	4.46410	+	7.73205i	0.209742	+	0.363283i
$454$	6.00000			0.281594
$455$		0			0
$456$	5.32051			0.249156
$457$	−15.3923	−	26.6603i	−0.720022	−	1.24711i	−0.960991	−	0.276581i	$-0.910799\pi$
$457$	−15.3923	−	26.6603i	−0.720022	−	1.24711i	0.240969	−	0.970533i	$-0.422535\pi$
$458$	12.4641	+	21.5885i	0.582409	+	1.00876i
$459$	−6.92820	+	12.0000i	−0.323381	+	0.560112i
$460$	4.73205			0.220633
$461$	1.73205	−	3.00000i	0.0806696	−	0.139724i	−0.822868	−	0.568232i	$-0.807627\pi$
$461$	1.73205	−	3.00000i	0.0806696	−	0.139724i	0.903538	+	0.428508i	$0.140961\pi$
$462$	1.60770	−	2.78461i	0.0747967	−	0.129552i
$463$	−18.3923			−0.854763			−0.427381	−	0.904071i	$-0.640564\pi$
$463$	−18.3923			−0.854763			−0.427381	+	0.904071i	$0.640564\pi$
$464$	−23.6603	+	40.9808i	−1.09840	+	1.90248i
$465$	0.0717968	+	0.124356i	0.00332950	+	0.00576686i
$466$	−5.19615	−	9.00000i	−0.240707	−	0.416917i
$467$	38.1962			1.76751			0.883754	−	0.467953i	$-0.155008\pi$
$467$	38.1962			1.76751			0.883754	+	0.467953i	$0.155008\pi$
$468$		0			0
$469$	−28.7846			−1.32915
$470$	−5.19615	−	9.00000i	−0.239681	−	0.415139i
$471$	−3.66025	−	6.33975i	−0.168656	−	0.292120i
$472$	−13.0981	+	22.6865i	−0.602888	+	1.04423i
$473$	12.9282			0.594439
$474$	−7.85641	+	13.6077i	−0.360857	+	0.625022i
$475$	2.09808	−	3.63397i	0.0962663	−	0.166738i
$476$	−6.92820			−0.317554
$477$	−12.8038	+	22.1769i	−0.586248	+	1.01541i
$478$	3.29423	+	5.70577i	0.150675	+	0.260976i
$479$	9.16987	+	15.8827i	0.418982	+	0.725698i	0.995837	−	0.0911480i	$-0.0290536\pi$
$479$	9.16987	+	15.8827i	0.418982	+	0.725698i	−0.576855	+	0.816846i	$0.695720\pi$
$480$	−3.80385			−0.173621
$481$		0			0
$482$	31.8564			1.45102
$483$	−3.46410	−	6.00000i	−0.157622	−	0.273009i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	26.4449			1.19956
$487$	−2.80385	+	4.85641i	−0.127054	+	0.220065i	−0.922534	−	0.385915i	$-0.873886\pi$
$487$	−2.80385	+	4.85641i	−0.127054	+	0.220065i	0.795480	+	0.605980i	$0.207219\pi$
$488$	−10.7321	+	18.5885i	−0.485817	+	0.841460i
$489$	4.67949			0.211614
$490$	−2.59808	+	4.50000i	−0.117369	+	0.203289i
$491$	4.73205	+	8.19615i	0.213554	+	0.369887i	0.952824	−	0.303522i	$-0.0981626\pi$
$491$	4.73205	+	8.19615i	0.213554	+	0.369887i	−0.739270	+	0.673409i	$0.764829\pi$
$492$	1.26795	+	2.19615i	0.0571636	+	0.0990102i
$493$	−32.7846			−1.47654
$494$		0			0
$495$	−3.12436			−0.140429
$496$	0.490381	+	0.849365i	0.0220188	+	0.0381376i
$497$	−1.26795	−	2.19615i	−0.0568753	−	0.0985109i
$498$	−3.80385	+	6.58846i	−0.170454	+	0.295236i
$499$	−12.9808			−0.581099			−0.290549	−	0.956860i	$-0.593838\pi$
$499$	−12.9808			−0.581099			−0.290549	+	0.956860i	$0.593838\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−4.73205	+	8.19615i	−0.211412	+	0.366177i
$502$	25.1769			1.12370
$503$	12.7583	−	22.0981i	0.568866	−	0.985305i	−0.427813	−	0.903867i	$-0.640716\pi$
$503$	12.7583	−	22.0981i	0.568866	−	0.985305i	0.996678	−	0.0814371i	$-0.0259510\pi$
$504$	−4.26795	−	7.39230i	−0.190110	−	0.329279i
$505$	−6.46410	−	11.1962i	−0.287649	−	0.498222i
$506$	−10.3923			−0.461994
$507$		0			0
$508$	5.80385			0.257504
$509$	16.2679	+	28.1769i	0.721064	+	1.24892i	0.960574	+	0.278026i	$0.0896801\pi$
$509$	16.2679	+	28.1769i	0.721064	+	1.24892i	−0.239509	+	0.970894i	$0.576987\pi$
$510$	−2.19615	−	3.80385i	−0.0972473	−	0.168437i
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$	−8.66025			−0.382733
$513$	8.39230	−	14.5359i	0.370529	−	0.641776i
$514$	−6.80385	+	11.7846i	−0.300105	+	0.519797i
$515$	10.1962			0.449296
$516$	3.73205	−	6.46410i	0.164294	−	0.284566i
$517$	3.80385	+	6.58846i	0.167293	+	0.289760i
$518$	−6.92820	−	12.0000i	−0.304408	−	0.527250i
$519$	−11.3205			−0.496915
$520$		0			0
$521$	−7.60770			−0.333299			−0.166650	−	0.986016i	$-0.553295\pi$
$521$	−7.60770			−0.333299			−0.166650	+	0.986016i	$0.553295\pi$
$522$	20.1962	+	34.9808i	0.883962	+	1.53107i
$523$	6.90192	+	11.9545i	0.301800	+	0.522733i	0.976544	−	0.215319i	$-0.0690792\pi$
$523$	6.90192	+	11.9545i	0.301800	+	0.522733i	−0.674744	+	0.738052i	$0.735746\pi$
$524$		0			0
$525$	1.46410			0.0638986
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	−0.339746	+	0.588457i	−0.0147996	+	0.0256336i
$528$	4.64102			0.201974
$529$	0.303848	−	0.526279i	0.0132108	−	0.0228817i
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$	18.6340	+	32.2750i	0.808646	+	1.40062i
$532$	8.39230			0.363853
$533$		0			0
$534$	−1.17691			−0.0509301
$535$	−0.169873	−	0.294229i	−0.00734425	−	0.0127206i
$536$	−12.4641	−	21.5885i	−0.538367	−	0.932479i
$537$	−1.85641	+	3.21539i	−0.0801099	+	0.138754i
$538$	−13.6077			−0.586669
$539$	1.90192	−	3.29423i	0.0819217	−	0.141892i
$540$	−2.00000	+	3.46410i	−0.0860663	+	0.149071i
$541$	5.60770			0.241094			0.120547	−	0.992708i	$-0.461535\pi$
$541$	5.60770			0.241094			0.120547	+	0.992708i	$0.461535\pi$
$542$	18.1699	−	31.4711i	0.780463	−	1.35180i
$543$	−7.46410	−	12.9282i	−0.320315	−	0.554802i
$544$	−9.00000	−	15.5885i	−0.385872	−	0.668350i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−1.80385			−0.0771270			−0.0385635	−	0.999256i	$-0.512278\pi$
$547$	−1.80385			−0.0771270			−0.0385635	+	0.999256i	$0.512278\pi$
$548$	−6.46410	−	11.1962i	−0.276133	−	0.478276i
$549$	15.2679	+	26.4449i	0.651620	+	1.12864i
$550$	1.09808	−	1.90192i	0.0468221	−	0.0810983i
$551$	39.7128			1.69182
$552$	3.00000	−	5.19615i	0.127688	−	0.221163i
$553$	12.3923	−	21.4641i	0.526974	−	0.912746i
$554$	9.71281			0.412658
$555$	1.46410	−	2.53590i	0.0621477	−	0.107643i
$556$	4.19615	+	7.26795i	0.177957	+	0.308230i
$557$	−12.9282	−	22.3923i	−0.547786	−	0.948792i	−0.998426	−	0.0560868i	$-0.982138\pi$
$557$	−12.9282	−	22.3923i	−0.547786	−	0.948792i	0.450640	−	0.892706i	$-0.351196\pi$
$558$	0.837169			0.0354402
$559$		0			0
$560$	10.0000			0.422577
$561$	1.60770	+	2.78461i	0.0678769	+	0.117566i
$562$	−1.39230	−	2.41154i	−0.0587308	−	0.101725i
$563$	−8.02628	+	13.9019i	−0.338267	+	0.585896i	−0.984107	−	0.177577i	$-0.943174\pi$
$563$	−8.02628	+	13.9019i	−0.338267	+	0.585896i	0.645840	+	0.763473i	$0.276507\pi$
$564$	4.39230			0.184949
$565$	−7.73205	+	13.3923i	−0.325290	+	0.563418i
$566$	1.22243	−	2.11731i	0.0513826	−	0.0889973i
$567$	−8.92820			−0.374949
$568$	1.09808	−	1.90192i	0.0460743	−	0.0798029i
$569$	4.73205	+	8.19615i	0.198378	+	0.343601i	0.948003	−	0.318263i	$-0.103099\pi$
$569$	4.73205	+	8.19615i	0.198378	+	0.343601i	−0.749625	+	0.661863i	$0.769766\pi$
$570$	2.66025	+	4.60770i	0.111426	+	0.192995i
$571$	15.6077			0.653162			0.326581	−	0.945169i	$-0.394103\pi$
$571$	15.6077			0.653162			0.326581	+	0.945169i	$0.394103\pi$
$572$		0			0
$573$	13.8564			0.578860
$574$	−6.00000	−	10.3923i	−0.250435	−	0.433766i
$575$	−2.36603	−	4.09808i	−0.0986701	−	0.170902i
$576$	1.23205	−	2.13397i	0.0513355	−	0.0889156i
$577$	4.00000			0.166522			0.0832611	−	0.996528i	$-0.473466\pi$
$577$	4.00000			0.166522			0.0832611	+	0.996528i	$0.473466\pi$
$578$	−4.33013	+	7.50000i	−0.180110	+	0.311959i
$579$	3.66025	−	6.33975i	0.152115	−	0.263471i
$580$	−9.46410			−0.392975
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	1.26795	+	2.19615i	0.0525582	+	0.0910334i
$583$	6.58846	+	11.4115i	0.272866	+	0.472618i
$584$	6.92820			0.286691
$585$		0			0
$586$	−32.7846			−1.35432
$587$	−7.73205	−	13.3923i	−0.319136	−	0.552760i	0.661172	−	0.750234i	$-0.270059\pi$
$587$	−7.73205	−	13.3923i	−0.319136	−	0.552760i	−0.980308	+	0.197475i	$0.936726\pi$
$588$	−1.09808	−	1.90192i	−0.0452839	−	0.0784340i
$589$	0.411543	−	0.712813i	0.0169573	−	0.0293709i
$590$	−26.1962			−1.07848
$591$	−0.339746	+	0.588457i	−0.0139753	+	0.0242059i
$592$	10.0000	−	17.3205i	0.410997	−	0.711868i
$593$	14.7846			0.607131			0.303566	−	0.952811i	$-0.401823\pi$
$593$	14.7846			0.607131			0.303566	+	0.952811i	$0.401823\pi$
$594$	4.39230	−	7.60770i	0.180218	−	0.312148i
$595$	3.46410	+	6.00000i	0.142014	+	0.245976i
$596$	9.92820	+	17.1962i	0.406675	+	0.704382i
$597$	−14.6410			−0.599217
$598$		0			0
$599$	−28.3923			−1.16008			−0.580039	−	0.814589i	$-0.696963\pi$
$599$	−28.3923			−1.16008			−0.580039	+	0.814589i	$0.696963\pi$
$600$	0.633975	+	1.09808i	0.0258819	+	0.0448288i
$601$	19.7846	+	34.2679i	0.807031	+	1.39782i	0.914911	+	0.403655i	$0.132260\pi$
$601$	19.7846	+	34.2679i	0.807031	+	1.39782i	−0.107880	+	0.994164i	$0.534406\pi$
$602$	−17.6603	+	30.5885i	−0.719778	+	1.24669i
$603$	−35.4641			−1.44421
$604$	−6.09808	+	10.5622i	−0.248127	+	0.429769i
$605$	4.69615	−	8.13397i	0.190926	−	0.330693i
$606$	16.3923			0.665892
$607$	13.4904	−	23.3660i	0.547558	−	0.948398i	−0.450883	−	0.892583i	$-0.648891\pi$
$607$	13.4904	−	23.3660i	0.547558	−	0.948398i	0.998441	−	0.0558149i	$-0.0177757\pi$
$608$	10.9019	+	18.8827i	0.442131	+	0.765794i
$609$	6.92820	+	12.0000i	0.280745	+	0.486265i
$610$	−21.4641			−0.869056
$611$		0			0
$612$	−8.53590			−0.345043
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	0.999574	+	0.0291886i	$0.00929235\pi$
$613$	13.0000	+	22.5167i	0.525065	+	0.909439i	−0.474509	+	0.880251i	$0.657374\pi$
$614$	−19.7321	−	34.1769i	−0.796321	−	1.37927i
$615$	1.26795	−	2.19615i	0.0511286	−	0.0885574i
$616$	−4.39230			−0.176971
$617$	−10.8564	+	18.8038i	−0.437062	+	0.757014i	−0.997461	−	0.0712084i	$-0.977314\pi$
$617$	−10.8564	+	18.8038i	−0.437062	+	0.757014i	0.560399	+	0.828223i	$0.310648\pi$
$618$	−6.46410	+	11.1962i	−0.260024	+	0.450375i
$619$	44.9808			1.80793			0.903965	−	0.427607i	$-0.140643\pi$
$619$	44.9808			1.80793			0.903965	+	0.427607i	$0.140643\pi$
$620$	−0.0980762	+	0.169873i	−0.00393884	+	0.00682226i
$621$	−9.46410	−	16.3923i	−0.379781	−	0.657801i
$622$	3.80385	+	6.58846i	0.152520	+	0.264173i
$623$	1.85641			0.0743754
$624$		0			0
$625$	1.00000			0.0400000
$626$	5.53590	+	9.58846i	0.221259	+	0.383232i
$627$	−1.94744	−	3.37307i	−0.0777733	−	0.134707i
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	13.8564			0.552491
$630$	4.26795	−	7.39230i	0.170039	−	0.294516i
$631$	8.09808	−	14.0263i	0.322379	−	0.558377i	−0.658599	−	0.752494i	$-0.728851\pi$
$631$	8.09808	−	14.0263i	0.322379	−	0.558377i	0.980978	+	0.194117i	$0.0621840\pi$
$632$	21.4641			0.853796
$633$	2.92820	−	5.07180i	0.116386	−	0.201586i
$634$	−20.7846	−	36.0000i	−0.825462	−	1.42974i
$635$	−2.90192	−	5.02628i	−0.115159	−	0.199462i
$636$	7.60770			0.301665
$637$		0			0
$638$	20.7846			0.822871
$639$	−1.56218	−	2.70577i	−0.0617988	−	0.107039i
$640$	6.06218	+	10.5000i	0.239629	+	0.415049i
$641$	0.464102	−	0.803848i	0.0183309	−	0.0317501i	−0.856714	−	0.515791i	$-0.827498\pi$
$641$	0.464102	−	0.803848i	0.0183309	−	0.0317501i	0.875045	+	0.484041i	$0.160831\pi$
$642$	0.430781			0.0170016
$643$	17.3923	−	30.1244i	0.685886	−	1.18799i	−0.287272	−	0.957849i	$-0.592748\pi$
$643$	17.3923	−	30.1244i	0.685886	−	1.18799i	0.973158	−	0.230140i	$-0.0739183\pi$
$644$	4.73205	−	8.19615i	0.186469	−	0.322974i
$645$	−7.46410			−0.293899
$646$	−12.5885	+	21.8038i	−0.495286	+	0.857861i
$647$	8.02628	+	13.9019i	0.315546	+	0.546541i	0.979553	−	0.201185i	$-0.0644791\pi$
$647$	8.02628	+	13.9019i	0.315546	+	0.546541i	−0.664008	+	0.747726i	$0.731146\pi$
$648$	−3.86603	−	6.69615i	−0.151872	−	0.263050i
$649$	19.1769			0.752760
$650$		0			0
$651$	0.287187			0.0112557
$652$	3.19615	+	5.53590i	0.125171	+	0.216803i
$653$	9.92820	+	17.1962i	0.388521	+	0.672937i	0.992251	−	0.124251i	$-0.0396529\pi$
$653$	9.92820	+	17.1962i	0.388521	+	0.672937i	−0.603730	+	0.797189i	$0.706320\pi$
$654$	1.26795	−	2.19615i	0.0495807	−	0.0858764i
$655$		0			0
$656$	8.66025	−	15.0000i	0.338126	−	0.585652i
$657$	4.92820	−	8.53590i	0.192268	−	0.333017i
$658$	−20.7846			−0.810268
$659$	7.26795	−	12.5885i	0.283119	−	0.490377i	−0.689032	−	0.724731i	$-0.741964\pi$
$659$	7.26795	−	12.5885i	0.283119	−	0.490377i	0.972151	+	0.234354i	$0.0752975\pi$
$660$	0.464102	+	0.803848i	0.0180651	+	0.0312897i
$661$	−15.3923	−	26.6603i	−0.598691	−	1.03696i	−0.993015	−	0.117992i	$-0.962354\pi$
$661$	−15.3923	−	26.6603i	−0.598691	−	1.03696i	0.394323	−	0.918972i	$-0.370979\pi$
$662$	−49.5167			−1.92452
$663$		0			0
$664$	10.3923			0.403300
$665$	−4.19615	−	7.26795i	−0.162720	−	0.281839i
$666$	−8.53590	−	14.7846i	−0.330759	−	0.572892i
$667$	22.3923	−	38.7846i	0.867034	−	1.50175i
$668$	−12.9282			−0.500207
$669$	−0.732051	+	1.26795i	−0.0283027	+	0.0490217i
$670$	12.4641	−	21.5885i	0.481530	−	0.834035i
$671$	15.7128			0.606586
$672$	−3.80385	+	6.58846i	−0.146737	+	0.254155i
$673$	−3.19615	−	5.53590i	−0.123203	−	0.213393i	0.797826	−	0.602887i	$-0.205983\pi$
$673$	−3.19615	−	5.53590i	−0.123203	−	0.213393i	−0.921029	+	0.389494i	$0.872650\pi$
$674$	−4.85641	−	8.41154i	−0.187062	−	0.324001i
$675$	4.00000			0.153960
$676$		0			0
$677$	−10.3923			−0.399409			−0.199704	−	0.979856i	$-0.563998\pi$
$677$	−10.3923			−0.399409			−0.199704	+	0.979856i	$0.563998\pi$
$678$	−9.80385	−	16.9808i	−0.376514	−	0.652142i
$679$	−2.00000	−	3.46410i	−0.0767530	−	0.132940i
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$	2.53590			0.0971758
$682$	0.215390	−	0.373067i	0.00824772	−	0.0142855i
$683$	19.7321	−	34.1769i	0.755026	−	1.30774i	−0.190335	−	0.981719i	$-0.560958\pi$
$683$	19.7321	−	34.1769i	0.755026	−	1.30774i	0.945361	−	0.326024i	$-0.105709\pi$
$684$	10.3397			0.395350
$685$	−6.46410	+	11.1962i	−0.246981	+	0.427783i
$686$	17.3205	+	30.0000i	0.661300	+	1.14541i
$687$	5.26795	+	9.12436i	0.200985	+	0.348116i
$688$	−50.9808			−1.94362
$689$		0			0
$690$	6.00000			0.228416
$691$	22.8827	+	39.6340i	0.870498	+	1.50775i	0.861482	+	0.507788i	$0.169537\pi$
$691$	22.8827	+	39.6340i	0.870498	+	1.50775i	0.00901639	+	0.999959i	$0.497130\pi$
$692$	−7.73205	−	13.3923i	−0.293928	−	0.509099i
$693$	−3.12436	+	5.41154i	−0.118684	+	0.205568i
$694$	−20.1962			−0.766635
$695$	4.19615	−	7.26795i	0.159169	−	0.275689i
$696$	−6.00000	+	10.3923i	−0.227429	+	0.393919i
$697$	12.0000			0.454532
$698$	−5.53590	+	9.58846i	−0.209537	+	0.362928i
$699$	−2.19615	−	3.80385i	−0.0830661	−	0.143875i
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	42.0000			1.58632			0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000			1.58632			0.793159	+	0.609015i	$0.208435\pi$
$702$		0			0
$703$	−16.7846			−0.633044
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$	−2.19615	−	3.80385i	−0.0827119	−	0.143261i
$706$	−24.0000	+	41.5692i	−0.903252	+	1.56448i
$707$	−25.8564			−0.972430
$708$	5.53590	−	9.58846i	0.208052	−	0.360356i
$709$	4.80385	−	8.32051i	0.180412	−	0.312483i	−0.761609	−	0.648037i	$-0.775590\pi$
$709$	4.80385	−	8.32051i	0.180412	−	0.312483i	0.942021	+	0.335554i	$0.108923\pi$
$710$	2.19615			0.0824201
$711$	15.2679	−	26.4449i	0.572593	−	0.991760i
$712$	0.803848	+	1.39230i	0.0301255	+	0.0521788i
$713$	−0.464102	−	0.803848i	−0.0173807	−	0.0301043i
$714$	−8.78461			−0.328756
$715$		0			0
$716$	−5.07180			−0.189542
$717$	1.39230	+	2.41154i	0.0519966	+	0.0900607i
$718$	−7.09808	−	12.2942i	−0.264898	−	0.458817i
$719$	−0.928203	+	1.60770i	−0.0346161	+	0.0599569i	−0.882814	−	0.469722i	$-0.844354\pi$
$719$	−0.928203	+	1.60770i	−0.0346161	+	0.0599569i	0.848198	+	0.529679i	$0.177688\pi$
$720$	12.3205			0.459158
$721$	10.1962	−	17.6603i	0.379725	−	0.657702i
$722$	−1.20577	+	2.08846i	−0.0448742	+	0.0777243i
$723$	13.4641			0.500735
$724$	10.1962	−	17.6603i	0.378937	−	0.656338i
$725$	4.73205	+	8.19615i	0.175744	+	0.304397i
$726$	5.95448	+	10.3135i	0.220992	+	0.382769i
$727$	13.4115			0.497407			0.248703	−	0.968580i	$-0.419996\pi$
$727$	13.4115			0.497407			0.248703	+	0.968580i	$0.419996\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	3.46410	+	6.00000i	0.128212	+	0.222070i
$731$	−17.6603	−	30.5885i	−0.653188	−	1.13135i
$732$	4.53590	−	7.85641i	0.167652	−	0.290381i
$733$	−38.0000			−1.40356			−0.701781	−	0.712393i	$-0.747612\pi$
$733$	−38.0000			−1.40356			−0.701781	+	0.712393i	$0.747612\pi$
$734$	19.2224	−	33.2942i	0.709513	−	1.22891i
$735$	−1.09808	+	1.90192i	−0.0405032	+	0.0701535i
$736$	24.5885			0.906343
$737$	−9.12436	+	15.8038i	−0.336100	+	0.582142i
$738$	−7.39230	−	12.8038i	−0.272115	−	0.471316i
$739$	−3.90192	−	6.75833i	−0.143535	−	0.248609i	0.785291	−	0.619127i	$-0.212513\pi$
$739$	−3.90192	−	6.75833i	−0.143535	−	0.248609i	−0.928825	+	0.370518i	$0.879180\pi$
$740$	4.00000			0.147043
$741$		0			0
$742$	−36.0000			−1.32160
$743$	−21.9282	−	37.9808i	−0.804468	−	1.39338i	−0.916650	−	0.399691i	$-0.869117\pi$
$743$	−21.9282	−	37.9808i	−0.804468	−	1.39338i	0.112182	−	0.993688i	$-0.464216\pi$
$744$	0.124356	+	0.215390i	0.00455910	+	0.00789659i
$745$	9.92820	−	17.1962i	0.363741	−	0.630018i
$746$	17.3205			0.634149
$747$	7.39230	−	12.8038i	0.270470	−	0.468468i
$748$	−2.19615	+	3.80385i	−0.0802993	+	0.139082i
$749$	−0.679492			−0.0248281
$750$	−0.633975	+	1.09808i	−0.0231495	+	0.0400961i
$751$	−7.80385	−	13.5167i	−0.284766	−	0.493230i	0.687786	−	0.725913i	$-0.258583\pi$
$751$	−7.80385	−	13.5167i	−0.284766	−	0.493230i	−0.972553	+	0.232683i	$0.925249\pi$
$752$	−15.0000	−	25.9808i	−0.546994	−	0.947421i
$753$	10.6410			0.387780
$754$		0			0
$755$	12.1962			0.443863
$756$	4.00000	+	6.92820i	0.145479	+	0.251976i
$757$	−9.19615	−	15.9282i	−0.334240	−	0.578920i	0.649099	−	0.760704i	$-0.275146\pi$
$757$	−9.19615	−	15.9282i	−0.334240	−	0.578920i	−0.983339	+	0.181784i	$0.941813\pi$
$758$	28.5622	−	49.4711i	1.03743	−	1.79687i
$759$	−4.39230			−0.159431
$760$	3.63397	−	6.29423i	0.131818	−	0.228316i
$761$	3.92820	−	6.80385i	0.142397	−	0.246639i	−0.786002	−	0.618224i	$-0.787852\pi$
$761$	3.92820	−	6.80385i	0.142397	−	0.246639i	0.928399	+	0.371585i	$0.121186\pi$
$762$	7.35898			0.266588
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$	9.46410	+	16.3923i	0.342399	+	0.593053i
$765$	4.26795	+	7.39230i	0.154308	+	0.267269i
$766$	−1.60770			−0.0580884
$767$		0			0
$768$	−13.9090			−0.501897
$769$	−3.39230	−	5.87564i	−0.122330	−	0.211881i	0.798356	−	0.602185i	$-0.205703\pi$
$769$	−3.39230	−	5.87564i	−0.122330	−	0.211881i	−0.920686	+	0.390304i	$0.872370\pi$
$770$	−2.19615	−	3.80385i	−0.0791438	−	0.137081i
$771$	−2.87564	+	4.98076i	−0.103564	+	0.179378i
$772$	10.0000			0.359908
$773$	−3.46410	+	6.00000i	−0.124595	+	0.215805i	−0.921575	−	0.388201i	$-0.873097\pi$
$773$	−3.46410	+	6.00000i	−0.124595	+	0.215805i	0.796980	+	0.604006i	$0.206430\pi$
$774$	−21.7583	+	37.6865i	−0.782087	+	1.35461i
$775$	0.196152			0.00704600
$776$	1.73205	−	3.00000i	0.0621770	−	0.107694i
$777$	−2.92820	−	5.07180i	−0.105049	−	0.181950i
$778$	5.19615	+	9.00000i	0.186291	+	0.322666i
$779$	−14.5359			−0.520803
$780$		0			0
$781$	−1.60770			−0.0575279
$782$	14.1962	+	24.5885i	0.507653	+	0.879281i
$783$	18.9282	+	32.7846i	0.676439	+	1.17163i
$784$	−7.50000	+	12.9904i	−0.267857	+	0.463942i
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−25.7846	+	44.6603i	−0.919122	+	1.59197i	−0.118371	+	0.992969i	$0.537767\pi$
$787$	−25.7846	+	44.6603i	−0.919122	+	1.59197i	−0.800752	+	0.598997i	$0.795566\pi$
$788$	−0.928203			−0.0330659
$789$	1.73205	−	3.00000i	0.0616626	−	0.106803i
$790$	10.7321	+	18.5885i	0.381829	+	0.661348i
$791$	15.4641	+	26.7846i	0.549840	+	0.952351i
$792$	−5.41154			−0.192291
$793$		0			0
$794$	−22.1436			−0.785847
$795$	−3.80385	−	6.58846i	−0.134909	−	0.233668i
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	−14.3205	+	24.8038i	−0.507258	+	0.878597i	0.492706	+	0.870196i	$0.336008\pi$
$797$	−14.3205	+	24.8038i	−0.507258	+	0.878597i	−0.999965	+	0.00840168i	$0.997326\pi$
$798$	10.6410			0.376688
$799$	10.3923	−	18.0000i	0.367653	−	0.636794i
$800$	−2.59808	+	4.50000i	−0.0918559	+	0.159099i
$801$	2.28719			0.0808138
$802$	19.9808	−	34.6077i	0.705545	−	1.22204i
$803$	−2.53590	−	4.39230i	−0.0894899	−	0.155001i
$804$	5.26795	+	9.12436i	0.185786	+	0.321791i
$805$	−9.46410			−0.333566
$806$		0			0
$807$	−5.75129			−0.202455
$808$	−11.1962	−	19.3923i	−0.393879	−	0.682219i
$809$	4.73205	+	8.19615i	0.166370	+	0.288161i	0.937141	−	0.348951i	$-0.113462\pi$
$809$	4.73205	+	8.19615i	0.166370	+	0.288161i	−0.770771	+	0.637112i	$0.780129\pi$
$810$	3.86603	−	6.69615i	0.135838	−	0.235279i
$811$	−28.1962			−0.990101			−0.495050	−	0.868864i	$-0.664850\pi$
$811$	−28.1962			−0.990101			−0.495050	+	0.868864i	$0.664850\pi$
$812$	−9.46410	+	16.3923i	−0.332125	+	0.575257i
$813$	7.67949	−	13.3013i	0.269332	−	0.466496i
$814$	−8.78461			−0.307900
$815$	3.19615	−	5.53590i	0.111956	−	0.193914i
$816$	−6.33975	−	10.9808i	−0.221936	−	0.384404i
$817$	21.3923	+	37.0526i	0.748422	+	1.29630i
$818$	−66.4974			−2.32503
$819$		0			0
$820$	3.46410			0.120972
$821$	−20.3205	−	35.1962i	−0.709191	−	1.22835i	−0.965158	−	0.261669i	$-0.915727\pi$
$821$	−20.3205	−	35.1962i	−0.709191	−	1.22835i	0.255967	−	0.966685i	$-0.417606\pi$
$822$	−8.19615	−	14.1962i	−0.285874	−	0.495148i
$823$	23.2942	−	40.3468i	0.811986	−	1.40640i	−0.0994864	−	0.995039i	$-0.531720\pi$
$823$	23.2942	−	40.3468i	0.811986	−	1.40640i	0.911472	−	0.411362i	$-0.134947\pi$
$824$	17.6603			0.615224
$825$	0.464102	−	0.803848i	0.0161579	−	0.0279864i
$826$	−26.1962	+	45.3731i	−0.911481	+	1.57873i
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$	5.83013	−	10.0981i	0.202611	−	0.350932i
$829$	10.1962	+	17.6603i	0.354127	+	0.613366i	0.986968	−	0.160916i	$-0.0514447\pi$
$829$	10.1962	+	17.6603i	0.354127	+	0.613366i	−0.632841	+	0.774282i	$0.718111\pi$
$830$	5.19615	+	9.00000i	0.180361	+	0.312395i
$831$	4.10512			0.142405
$832$		0			0
$833$	−10.3923			−0.360072
$834$	5.32051	+	9.21539i	0.184234	+	0.319103i
$835$	6.46410	+	11.1962i	0.223699	+	0.387459i
$836$	2.66025	−	4.60770i	0.0920068	−	0.159360i
$837$	0.784610			0.0271201
$838$	−8.19615	+	14.1962i	−0.283131	+	0.490398i
$839$	8.83013	−	15.2942i	0.304850	−	0.528015i	−0.672378	−	0.740208i	$-0.734727\pi$
$839$	8.83013	−	15.2942i	0.304850	−	0.528015i	0.977228	+	0.212193i	$0.0680604\pi$
$840$	2.53590			0.0874968
$841$	−30.2846	+	52.4545i	−1.04430	+	1.80878i
$842$	−9.33975	−	16.1769i	−0.321869	−	0.557493i
$843$	−0.588457	−	1.01924i	−0.0202675	−	0.0351044i
$844$	8.00000			0.275371
$845$		0			0
$846$	−25.6077			−0.880411
$847$	−9.39230	−	16.2679i	−0.322723	−	0.558973i
$848$	−25.9808	−	45.0000i	−0.892183	−	1.54531i
$849$	0.516660	−	0.894882i	0.0177317	−	0.0307123i
$850$	−6.00000			−0.205798
$851$	−9.46410	+	16.3923i	−0.324425	+	0.561921i
$852$	−0.464102	+	0.803848i	−0.0158999	+	0.0275394i
$853$	−8.00000			−0.273915			−0.136957	−	0.990577i	$-0.543732\pi$
$853$	−8.00000			−0.273915			−0.136957	+	0.990577i	$0.543732\pi$
$854$	−21.4641	+	37.1769i	−0.734486	+	1.27217i
$855$	−5.16987	−	8.95448i	−0.176806	−	0.306237i
$856$	−0.294229	−	0.509619i	−0.0100565	−	0.0174184i
$857$	47.5692			1.62493			0.812467	−	0.583007i	$-0.198124\pi$
$857$	47.5692			1.62493			0.812467	+	0.583007i	$0.198124\pi$
$858$		0			0
$859$	45.1769			1.54142			0.770708	−	0.637188i	$-0.219903\pi$
$859$	45.1769			1.54142			0.770708	+	0.637188i	$0.219903\pi$
$860$	−5.09808	−	8.83013i	−0.173843	−	0.301105i
$861$	−2.53590	−	4.39230i	−0.0864232	−	0.149689i
$862$	−16.9019	+	29.2750i	−0.575682	+	0.997110i
$863$	−2.78461			−0.0947892			−0.0473946	−	0.998876i	$-0.515092\pi$
$863$	−2.78461			−0.0947892			−0.0473946	+	0.998876i	$0.515092\pi$
$864$	−10.3923	+	18.0000i	−0.353553	+	0.612372i
$865$	−7.73205	+	13.3923i	−0.262898	+	0.455352i
$866$	11.7513			0.399325
$867$	−1.83013	+	3.16987i	−0.0621544	+	0.107655i
$868$	0.196152	+	0.339746i	0.00665785	+	0.0115317i
$869$	−7.85641	−	13.6077i	−0.266510	−	0.461609i
$870$	−12.0000			−0.406838
$871$		0			0
$872$	−3.46410			−0.117309
$873$	−2.46410	−	4.26795i	−0.0833972	−	0.144448i
$874$	−17.1962	−	29.7846i	−0.581669	−	1.00748i
$875$	1.00000	−	1.73205i	0.0338062	−	0.0585540i
$876$	−2.92820			−0.0989348
$877$	1.00000	−	1.73205i	0.0337676	−	0.0584872i	−0.848648	−	0.528958i	$-0.822583\pi$
$877$	1.00000	−	1.73205i	0.0337676	−	0.0584872i	0.882415	+	0.470471i	$0.155916\pi$
$878$	27.7128	−	48.0000i	0.935262	−	1.61992i
$879$	−13.8564			−0.467365
$880$	3.16987	−	5.49038i	0.106856	−	0.185081i
$881$	6.33975	+	10.9808i	0.213591	+	0.369951i	0.952836	−	0.303486i	$-0.0981505\pi$
$881$	6.33975	+	10.9808i	0.213591	+	0.369951i	−0.739244	+	0.673437i	$0.764817\pi$
$882$	6.40192	+	11.0885i	0.215564	+	0.373368i
$883$	34.1962			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$883$	34.1962			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$884$		0			0
$885$	−11.0718			−0.372174
$886$	30.2942	+	52.4711i	1.01775	+	1.76280i
$887$	−8.95448	−	15.5096i	−0.300662	−	0.520762i	0.675624	−	0.737246i	$-0.263874\pi$
$887$	−8.95448	−	15.5096i	−0.300662	−	0.520762i	−0.976286	+	0.216484i	$0.930541\pi$
$888$	2.53590	−	4.39230i	0.0850992	−	0.147396i
$889$	−11.6077			−0.389310
$890$	−0.803848	+	1.39230i	−0.0269450	+	0.0466702i
$891$	−2.83013	+	4.90192i	−0.0948128	+	0.164221i
$892$	−2.00000			−0.0669650
$893$	−12.5885	+	21.8038i	−0.421257	+	0.729638i
$894$	12.5885	+	21.8038i	0.421021	+	0.729230i
$895$	2.53590	+	4.39230i	0.0847657	+	0.146819i
$896$	24.2487			0.810093
$897$		0			0
$898$	47.5692			1.58741
$899$	0.928203	+	1.60770i	0.0309573	+	0.0536196i
$900$	1.23205	+	2.13397i	0.0410684	+	0.0711325i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$	−7.60770			−0.253309
$903$	−7.46410	+	12.9282i	−0.248390	+	0.430224i
$904$	−13.3923	+	23.1962i	−0.445421	+	0.771493i
$905$	−20.3923			−0.677863
$906$	−7.73205	+	13.3923i	−0.256880	+	0.444930i
$907$	−19.8827	−	34.4378i	−0.660194	−	1.14349i	−0.980565	−	0.196197i	$-0.937141\pi$
$907$	−19.8827	−	34.4378i	−0.660194	−	1.14349i	0.320371	−	0.947292i	$-0.396193\pi$
$908$	1.73205	+	3.00000i	0.0574801	+	0.0995585i
$909$	−31.8564			−1.05661
$910$		0			0
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	7.67949	+	13.3013i	0.254293	+	0.440449i
$913$	−3.80385	−	6.58846i	−0.125889	−	0.218046i
$914$	26.6603	−	46.1769i	0.881843	−	1.52740i
$915$	−9.07180			−0.299904
$916$	−7.19615	+	12.4641i	−0.237768	+	0.411826i
$917$		0			0
$918$	−24.0000			−0.792118
$919$	26.5885	−	46.0526i	0.877072	−	1.51913i	0.0225335	−	0.999746i	$-0.492827\pi$
$919$	26.5885	−	46.0526i	0.877072	−	1.51913i	0.854539	−	0.519388i	$-0.173840\pi$
$920$	−4.09808	−	7.09808i	−0.135110	−	0.234017i
$921$	−8.33975	−	14.4449i	−0.274804	−	0.475974i
$922$	6.00000			0.197599
$923$		0			0
$924$	1.85641			0.0610713
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	−15.9282	−	27.5885i	−0.523433	−	0.906613i
$927$	12.5622	−	21.7583i	0.412596	−	0.714637i
$928$	−49.1769			−1.61431
$929$	25.7321	−	44.5692i	0.844241	−	1.46227i	−0.0420373	−	0.999116i	$-0.513385\pi$
$929$	25.7321	−	44.5692i	0.844241	−	1.46227i	0.886279	−	0.463153i	$-0.153282\pi$
$930$	−0.124356	+	0.215390i	−0.00407778	+	0.00706293i
$931$	12.5885			0.412570
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	1.60770	+	2.78461i	0.0526336	+	0.0911640i
$934$	33.0788	+	57.2942i	1.08237	+	1.87472i
$935$	4.39230			0.143644
$936$		0			0
$937$	−6.78461			−0.221644			−0.110822	−	0.993840i	$-0.535348\pi$
$937$	−6.78461			−0.221644			−0.110822	+	0.993840i	$0.535348\pi$
$938$	−24.9282	−	43.1769i	−0.813935	−	1.40978i
$939$	2.33975	+	4.05256i	0.0763547	+	0.132250i
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	31.1769			1.01634			0.508169	−	0.861257i	$-0.330322\pi$
$941$	31.1769			1.01634			0.508169	+	0.861257i	$0.330322\pi$
$942$	6.33975	−	10.9808i	0.206560	−	0.357773i
$943$	−8.19615	+	14.1962i	−0.266903	+	0.462290i
$944$	−75.6218			−2.46128
$945$	4.00000	−	6.92820i	0.130120	−	0.225374i
$946$	11.1962	+	19.3923i	0.364018	+	0.630498i
$947$	−14.3205	−	24.8038i	−0.465354	−	0.806017i	0.533863	−	0.845571i	$-0.320740\pi$
$947$	−14.3205	−	24.8038i	−0.465354	−	0.806017i	−0.999217	+	0.0395540i	$0.987406\pi$
$948$	−9.07180			−0.294638
$949$		0			0
$950$	7.26795			0.235803
$951$	−8.78461	−	15.2154i	−0.284860	−	0.493393i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	6.46410	−	11.1962i	0.209393	−	0.362679i	−0.742131	−	0.670255i	$-0.766185\pi$
$953$	6.46410	−	11.1962i	0.209393	−	0.362679i	0.951523	+	0.307576i	$0.0995179\pi$
$954$	−44.3538			−1.43601
$955$	9.46410	−	16.3923i	0.306251	−	0.530443i
$956$	−1.90192	+	3.29423i	−0.0615126	+	0.106543i
$957$	8.78461			0.283966
$958$	−15.8827	+	27.5096i	−0.513146	+	0.888795i
$959$	12.9282	+	22.3923i	0.417473	+	0.723085i
$960$	0.366025	+	0.633975i	0.0118134	+	0.0204614i
$961$	−30.9615			−0.998759
$962$		0			0
$963$	−0.837169			−0.0269774
$964$	9.19615	+	15.9282i	0.296188	+	0.513013i
$965$	−5.00000	−	8.66025i	−0.160956	−	0.278783i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	29.6077			0.952119			0.476060	−	0.879413i	$-0.342065\pi$
$967$	29.6077			0.952119			0.476060	+	0.879413i	$0.342065\pi$
$968$	8.13397	−	14.0885i	0.261436	−	0.452820i
$969$	−5.32051	+	9.21539i	−0.170919	+	0.296041i
$970$	3.46410			0.111226
$971$	−2.53590	+	4.39230i	−0.0813809	+	0.140956i	−0.903843	−	0.427864i	$-0.859266\pi$
$971$	−2.53590	+	4.39230i	−0.0813809	+	0.140956i	0.822462	+	0.568819i	$0.192600\pi$
$972$	7.63397	+	13.2224i	0.244860	+	0.424110i
$973$	−8.39230	−	14.5359i	−0.269045	−	0.466000i
$974$	−9.71281			−0.311219
$975$		0			0
$976$	−61.9615			−1.98334
$977$	19.8564	+	34.3923i	0.635263	+	1.10031i	0.986459	+	0.164006i	$0.0524415\pi$
$977$	19.8564	+	34.3923i	0.635263	+	1.10031i	−0.351197	+	0.936302i	$0.614225\pi$
$978$	4.05256	+	7.01924i	0.129587	+	0.224450i
$979$	0.588457	−	1.01924i	0.0188072	−	0.0325750i
$980$	−3.00000			−0.0958315
$981$	−2.46410	+	4.26795i	−0.0786727	+	0.136265i
$982$	−8.19615	+	14.1962i	−0.261550	+	0.453017i
$983$	13.6077			0.434018			0.217009	−	0.976170i	$-0.430370\pi$
$983$	13.6077			0.434018			0.217009	+	0.976170i	$0.430370\pi$
$984$	2.19615	−	3.80385i	0.0700108	−	0.121262i
$985$	0.464102	+	0.803848i	0.0147875	+	0.0256127i
$986$	−28.3923	−	49.1769i	−0.904195	−	1.56611i
$987$	−8.78461			−0.279617
$988$		0			0
$989$	48.2487			1.53422
$990$	−2.70577	−	4.68653i	−0.0859951	−	0.148948i
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	−0.509619	+	0.882686i	−0.0161804	+	0.0280253i
$993$	−20.9282			−0.664136
$994$	2.19615	−	3.80385i	0.0696577	−	0.120651i
$995$	−10.0000	+	17.3205i	−0.317021	+	0.549097i
$996$	−4.39230			−0.139176
$997$	−27.1962	+	47.1051i	−0.861311	+	1.49183i	0.00935346	+	0.999956i	$0.497023\pi$
$997$	−27.1962	+	47.1051i	−0.861311	+	1.49183i	−0.870664	+	0.491878i	$0.836311\pi$
$998$	−11.2417	−	19.4711i	−0.355849	−	0.616348i
$999$	−8.00000	−	13.8564i	−0.253109	−	0.438397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.e.f.146.2		4
13.2	odd	12		845.2.c.e.506.3		4
13.3	even	3		845.2.a.d.1.1		2
13.4	even	6		845.2.e.e.191.1		4
13.5	odd	4		845.2.m.c.361.2		4
13.6	odd	12		845.2.m.a.316.2		4
13.7	odd	12		845.2.m.c.316.2		4
13.8	odd	4		845.2.m.a.361.2		4
13.9	even	3	inner	845.2.e.f.191.2		4
13.10	even	6		65.2.a.c.1.2	✓	2
13.11	odd	12		845.2.c.e.506.1		4
13.12	even	2		845.2.e.e.146.1		4
39.23	odd	6		585.2.a.k.1.1		2
39.29	odd	6		7605.2.a.be.1.2		2
52.23	odd	6		1040.2.a.h.1.2		2
65.23	odd	12		325.2.b.e.274.2		4
65.29	even	6		4225.2.a.w.1.2		2
65.49	even	6		325.2.a.g.1.1		2
65.62	odd	12		325.2.b.e.274.3		4
91.62	odd	6		3185.2.a.k.1.2		2
104.75	odd	6		4160.2.a.bj.1.1		2
104.101	even	6		4160.2.a.y.1.2		2
143.10	odd	6		7865.2.a.h.1.1		2
156.23	even	6		9360.2.a.cm.1.2		2
195.23	even	12		2925.2.c.v.2224.3		4
195.62	even	12		2925.2.c.v.2224.2		4
195.179	odd	6		2925.2.a.z.1.2		2
260.179	odd	6		5200.2.a.ca.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.a.c.1.2	✓	2	13.10	even	6
325.2.a.g.1.1		2	65.49	even	6
325.2.b.e.274.2		4	65.23	odd	12
325.2.b.e.274.3		4	65.62	odd	12
585.2.a.k.1.1		2	39.23	odd	6
845.2.a.d.1.1		2	13.3	even	3
845.2.c.e.506.1		4	13.11	odd	12
845.2.c.e.506.3		4	13.2	odd	12
845.2.e.e.146.1		4	13.12	even	2
845.2.e.e.191.1		4	13.4	even	6
845.2.e.f.146.2		4	1.1	even	1	trivial
845.2.e.f.191.2		4	13.9	even	3	inner
845.2.m.a.316.2		4	13.6	odd	12
845.2.m.a.361.2		4	13.8	odd	4
845.2.m.c.316.2		4	13.7	odd	12
845.2.m.c.361.2		4	13.5	odd	4
1040.2.a.h.1.2		2	52.23	odd	6
2925.2.a.z.1.2		2	195.179	odd	6
2925.2.c.v.2224.2		4	195.62	even	12
2925.2.c.v.2224.3		4	195.23	even	12
3185.2.a.k.1.2		2	91.62	odd	6
4160.2.a.y.1.2		2	104.101	even	6
4160.2.a.bj.1.1		2	104.75	odd	6
4225.2.a.w.1.2		2	65.29	even	6
5200.2.a.ca.1.1		2	260.179	odd	6
7605.2.a.be.1.2		2	39.29	odd	6
7865.2.a.h.1.1		2	143.10	odd	6
9360.2.a.cm.1.2		2	156.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.633975 + 1.09808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-0.633975 + 1.09808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-0.633975 - 1.09808i) q^{11} -0.732051 q^{12} +3.46410 q^{14} +(0.366025 + 0.633975i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-1.73205 + 3.00000i) q^{17} +4.26795 q^{18} +(2.09808 - 3.63397i) q^{19} +(-0.500000 + 0.866025i) q^{20} +1.46410 q^{21} +(1.09808 - 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(0.633975 + 1.09808i) q^{24} +1.00000 q^{25} +4.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.73205 + 8.19615i) q^{29} +(-0.633975 + 1.09808i) q^{30} +0.196152 q^{31} +(-2.59808 + 4.50000i) q^{32} +(0.464102 - 0.803848i) q^{33} -6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(1.23205 + 2.13397i) q^{36} +(-2.00000 - 3.46410i) q^{37} +7.26795 q^{38} +1.73205 q^{40} +(-1.73205 - 3.00000i) q^{41} +(1.26795 + 2.19615i) q^{42} +(-5.09808 + 8.83013i) q^{43} +1.26795 q^{44} +(1.23205 - 2.13397i) q^{45} +(4.09808 - 7.09808i) q^{46} -6.00000 q^{47} +(-1.83013 + 3.16987i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.866025 + 1.50000i) q^{50} -2.53590 q^{51} -10.3923 q^{53} +(3.46410 + 6.00000i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(1.73205 - 3.00000i) q^{56} +3.07180 q^{57} +(-8.19615 + 14.1962i) q^{58} +(-7.56218 + 13.0981i) q^{59} -0.732051 q^{60} +(-6.19615 + 10.7321i) q^{61} +(0.169873 + 0.294229i) q^{62} +(-2.46410 - 4.26795i) q^{63} +1.00000 q^{64} +1.60770 q^{66} +(-7.19615 - 12.4641i) q^{67} +(-1.73205 - 3.00000i) q^{68} +(1.73205 - 3.00000i) q^{69} +3.46410 q^{70} +(0.633975 - 1.09808i) q^{71} +(2.13397 - 3.69615i) q^{72} +4.00000 q^{73} +(3.46410 - 6.00000i) q^{74} +(0.366025 + 0.633975i) q^{75} +(2.09808 + 3.63397i) q^{76} -2.53590 q^{77} +12.3923 q^{79} +(2.50000 + 4.33013i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-0.732051 + 1.26795i) q^{84} +(-1.73205 + 3.00000i) q^{85} -17.6603 q^{86} +(-3.46410 + 6.00000i) q^{87} +(-1.09808 - 1.90192i) q^{88} +(0.464102 + 0.803848i) q^{89} +4.26795 q^{90} +4.73205 q^{92} +(0.0717968 + 0.124356i) q^{93} +(-5.19615 - 9.00000i) q^{94} +(2.09808 - 3.63397i) q^{95} -3.80385 q^{96} +(1.00000 - 1.73205i) q^{97} +(-2.59808 + 4.50000i) q^{98} -3.12436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} + 4 q^{5} - 6 q^{6} + 4 q^{7} - 2 q^{9} - 6 q^{11} + 4 q^{12} - 2 q^{15} + 10 q^{16} + 24 q^{18} - 2 q^{19} - 2 q^{20} - 8 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} + 4 q^{25} + 16 q^{27} + 4 q^{28} + 12 q^{29} - 6 q^{30} - 20 q^{31} - 12 q^{33} - 24 q^{34} + 4 q^{35} - 2 q^{36} - 8 q^{37} + 36 q^{38} + 12 q^{42} - 10 q^{43} + 12 q^{44} - 2 q^{45} + 6 q^{46} - 24 q^{47} + 10 q^{48} + 6 q^{49} - 24 q^{51} - 6 q^{55} + 40 q^{57} - 12 q^{58} - 6 q^{59} + 4 q^{60} - 4 q^{61} + 18 q^{62} + 4 q^{63} + 4 q^{64} + 48 q^{66} - 8 q^{67} + 6 q^{71} + 12 q^{72} + 16 q^{73} - 2 q^{75} - 2 q^{76} - 24 q^{77} + 8 q^{79} + 10 q^{80} - 2 q^{81} + 12 q^{82} + 24 q^{83} + 4 q^{84} - 36 q^{86} + 6 q^{88} - 12 q^{89} + 24 q^{90} + 12 q^{92} + 28 q^{93} - 2 q^{95} - 36 q^{96} + 4 q^{97} + 36 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 + 4 * q^5 - 6 * q^6 + 4 * q^7 - 2 * q^9 - 6 * q^11 + 4 * q^12 - 2 * q^15 + 10 * q^16 + 24 * q^18 - 2 * q^19 - 2 * q^20 - 8 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 + 4 * q^25 + 16 * q^27 + 4 * q^28 + 12 * q^29 - 6 * q^30 - 20 * q^31 - 12 * q^33 - 24 * q^34 + 4 * q^35 - 2 * q^36 - 8 * q^37 + 36 * q^38 + 12 * q^42 - 10 * q^43 + 12 * q^44 - 2 * q^45 + 6 * q^46 - 24 * q^47 + 10 * q^48 + 6 * q^49 - 24 * q^51 - 6 * q^55 + 40 * q^57 - 12 * q^58 - 6 * q^59 + 4 * q^60 - 4 * q^61 + 18 * q^62 + 4 * q^63 + 4 * q^64 + 48 * q^66 - 8 * q^67 + 6 * q^71 + 12 * q^72 + 16 * q^73 - 2 * q^75 - 2 * q^76 - 24 * q^77 + 8 * q^79 + 10 * q^80 - 2 * q^81 + 12 * q^82 + 24 * q^83 + 4 * q^84 - 36 * q^86 + 6 * q^88 - 12 * q^89 + 24 * q^90 + 12 * q^92 + 28 * q^93 - 2 * q^95 - 36 * q^96 + 4 * q^97 + 36 * q^99

Introduction

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